Synapse Stats: Synapse Exploration on Lin F0

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The formatted source code for this file is here.
And a raw version here.
Previous work by Youngser Park can be found here.

We now have the following data sets:

• featF0: The feature vector looking only at the integrated brightness features.
• fs: The feature vector scaled between \([0,1000]\).

1 Level 0

dat <- fs

1.1 Heat maps (Lv 0):

## Formatting data for heatmap
aggp <- apply(dat, 2, mean)
aggp <- t(cbind(aggp, aggp))[, ford]

The following are heatmaps generated from clustering via K-means++ (at level 1)

heatmap.2(as.matrix(aggp),dendrogram='none',Colv=NA,trace="none", 
          col=mycol,colCol=ccol[ford],cexRow=0.8, keysize=1.25,symkey=FALSE,
          symbreaks=FALSE,scale="none", srtCol=90,main="Heatmap of `fs` data.", 
          labRow = "") 

Figure 1: Heatmap of the cluster means vs channels. Rows and columns are rearranged according to synapse type.

Percentage of data within cluster is presented on the right side of the heatmap.

1.2 Jittered scatter plot: Lv 0

set.seed(1024)
s2 <- sample(dim(dat)[1], 1e4)
ggJdat <- data.table(cbind(stack(dat[s2]),L[s2]))
ggJdat$ind <- as.factor(ggJdat$ind)
levels(ggJdat$ind) <- names(dat)[ford]

ggJ0 <- 
  ggplot(data = ggJdat, aes(x = ind, y = values)) +
  geom_point(alpha=0.75) + 
  geom_jitter(width = 1) + 
  geom_boxplot(alpha =0.35, outlier.color = 'NA') + 
  theme(axis.title.x = element_blank()) + 
  theme(axis.text.x = element_text(color = ccol[ford], 
                                   angle=45,
                                   vjust = 0.5))

print(ggJ0)

Figure 2: Scatter Plot Level 0

The above scatter plot is a random sample of the data points.

1.3 Correlations: Lv 0

cmatfs <- cor(fs)[ford, ford]
corrplot(cmatfs,method="color",tl.col=ccol[ford], tl.cex=1)

Figure 3: Correlation on untransformed F0 data, reordered by synapse type.

1.3.1 PCA of the within cluster correlation matrices at level 0.

pcaL0 <- prcomp(cmatfs, center=TRUE, scale=TRUE)

1.3.1.1 PCA Lv0

pca0 <- data.frame(pcaL0$x)
rgl::plot3d(pca0[,1],pca0[,2],pca0[,3],type='s',col=ccol3[ford], size=1,
            xlab = "PC1", ylab = "PC2", zlab = "PC3")
rgl::rgl.texts(pca0[,1],pca0[,2],pca0[,3],abbreviate(rownames(pca0)), col=ccol3[ford], adj=c(0,2))
title3d(main = "Lv 0")
subid <- currentSubscene3d()
rglwidget(elementId="rgl-pca0",width=720,height=720)

1.3.2 LDA on Lv 0

Using LDA with re-substitution to create a voronoi diagram for Lv 0.

tr <- factor(exType, ordered = FALSE)
lda.fit0 <- lda(tr ~ ., data = pca0[, 1:10])
lda.pred0 <- predict(lda.fit0)

titlesvor <- paste("LDA decision boundaries for", paste0("F", 0:5))
voronoidf <- data.frame(lda.fit0$means)
#voronoidf <- data.frame(x=lda.fit$means[,1],y=lda.fit$means[,2])

#This creates the voronoi line segments

plot(pca0[,1:2], col=ccol3[ford], pch=20, cex=1.5, xlim =
     c(min(pca0[,1:2]) -3, 5))
text(pca0[,1:2], labels=rownames(pca0), 
     pos=ifelse(exType %in% c('ex', 'in'), 2, 4), 
     col=ccol3[ford], cex=1.2)

deldir(x = voronoidf[,1],y = voronoidf[,2], 
       rw = c(-15,15,-15,15), 
       plotit=TRUE, add=TRUE, wl='te')
text(voronoidf[,1:2], labels=rownames(voronoidf), cex=1.25, pos=2)

1.3.3 Mean-difference space projections

Staring from the correlation matrix cmatfs we compute the class means; \(v_1 = column\_mean(\)Excitatory\()\), \(v_2 = column\_mean(\)Inhibatory\()\), \(v_3 = column\_mean(\)Other\()\).

We then compute \(r_1 = v_1 - v_2\) and \(r_2 = v_1 - v_3\).

We then multiply \([cmatfs] \cdot [r_1 |\, r_2]\). The transformed points are then plotted below.

exMat <- cmatfs[exType == 'ex',]
inMat <- cmatfs[exType == 'in',]
otMat <- cmatfs[exType == 'other',]

mEx <- apply(exMat, 2, mean)
mIn <- apply(inMat, 2, mean)
mOt <- apply(otMat, 2, mean)

mXI <- mEx - mIn
mXO <- mEx - mOt

rotM <- data.frame(XI = mXI, XO = mXO)

mdm <- cmatfs %*% as.matrix(rotM)

plot(mdm, col = ccol3[ford], pch = 20, cex=3, type = 'n')
abline(h = 0, v = 0)
text(mdm, labels=rownames(mdm), col=ccol3[ford], cex = 0.75)

lm.fit <- lm(mdm[,2] ~ mdm[,1])
abline(a = lm.fit$coefficients[1], b = lm.fit$coefficients[2], col =
       'darkorange', lty=2)
legend(list(x= -1.5,y=1.6), legend = c('regression line'), col = 'darkorange', lty=2)
title("Mean-difference projections of markers")

Figure 5: Mean-difference projections

2 Level 1: K-means++ for \(K=2\).

We run a Hierachical K-means++ for \(K=2\) on the fs data with 4 levels.

set.seed(2^13)
L <- bhkmpp(dat,blevels=4)

2.1 Heat maps (Lv 1):

## Formatting data for heatmap
aggp <- aggregate(dat,by=list(lab=L[[1]]),FUN=mean)
aggp <- as.matrix(aggp[,-1])[, ford]
rownames(aggp) <- clusterFraction(L[[1]])

The following are heatmaps generated from clustering via K-means++ (at level 1)

heatmap.2(as.matrix(aggp),dendrogram='row',Colv=NA,trace="none", col=mycol,colCol=ccol[ford],cexRow=0.8, keysize=1.25,symkey=FALSE,symbreaks=FALSE,scale="none", srtCol=90,main="Heatmap of `fs` data.") 

Figure 6: Heatmap of the cluster means vs channels. Rows and columns are rearranged according to synapse type.

Percentage of data within cluster is presented on the right side of the heatmap.

2.2 Jittered scatter plot: Lv 1

ggCol <- brewer.pal(4,"Set1")[order(table(L[[1]]))]

cf1 <- data.frame(cf = clusterFraction(L[[1]]))

ggJ1 <- 
  ggplot(data = ggJdat, aes(x = ind, y = values, 
                         color = as.factor(lv1))) +
  scale_color_manual(values=ggCol, name="Cluster") + 
  geom_point(alpha=0.25, position=position_jitterdodge()) + 
  geom_boxplot(alpha =0.35, outlier.color = 'NA') + 
  annotate("text", x = levels(ggJdat$ind)[c(2,20)], y = 1.15*max(ggJdat$values), 
           label= cf1[1:2,]) + 
  theme(axis.title.x = element_blank()) + 
  theme(axis.text.x = element_text(color = ccol[ford], 
                                   angle=45,
                                   vjust = 0.5))

print(ggJ1)

Figure 7: Scatter Plot Level 1

2.3 Within cluster correlations (Lv 1)

corkp1 <- cor(dat[L[[1]] == 1,])[ford, ford]
corkp2 <- cor(dat[L[[1]] == 2,])[ford, ford]
difCor12 <- (corkp1 - corkp2)

layout(matrix(c(1,2,3,3), 2, 2, byrow=TRUE))
corrplot(corkp1,method="color",tl.col=ccol[ford], tl.cex=0.8, mar=c(0,0,3,0))
title("Cluster 1")
corrplot(corkp2,method="color",tl.col=ccol[ford], tl.cex=0.8, mar=c(0,0,3,0))
title("Cluster 2")
corrplot(difCor12,is.corr=FALSE,method="color",
         tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,3,0),
         col=colorRampPalette(c("#998ec3","white","darkorange"))(50))
title("Difference(1,2)")

Figure 8: Within cluster correlations, clock-wise from top left, Cluster 1, Cluster 2, difference C1 - C2

Notice that the non-synaptic markers change very little between clusters. Also note that the correlations between (gad, VGAT, PV, Gephyr) and VGlut1 at both times change significantly between clusters.

Next we compute PCA for the within cluster correlation matrices and embed in 3d.

2.3.1 PCA of the within cluster correlation matrices at level 1.

pcaL <- lapply(list(corkp1, corkp2), prcomp, center=TRUE, scale=TRUE)
elB <- lapply(pcaL, function(x) {getElbows(x$sdev, plot=FALSE)})

2.3.1.1 PCA C1 Lv1

pca <- pcaL[[1]]$x
rgl::plot3d(pca[,1],pca[,2],pca[,3],type='s',col=ccol3[ford], size=1,
            xlab = "PC1", ylab = "PC2", zlab = "PC3")
rgl::rgl.texts(pca[,1],pca[,2],pca[,3],abbreviate(rownames(pca)), col=ccol3[ford], adj=c(0,2))
title3d(main = "Cluster 1: Lv 1")
subid <- currentSubscene3d()
rglwidget(elementId="rgl-pca1",width=720,height=720)

2.3.1.2 PCA C1 Lv1

pca <- pcaL[[2]]$x
rgl::plot3d(pca[,1],pca[,2],pca[,3],type='s',col=ccol3[ford], size=1,
            xlab = "PC1", ylab = "PC2", zlab = "PC3")
rgl::rgl.texts(pca[,1],pca[,2],pca[,3],abbreviate(rownames(pca)), col=ccol3[ford], adj=c(0,2))
title3d(main = "Cluster 2: Lv 1")
subid <- currentSubscene3d()
rglwidget(elementId="rgl-pca2",width=720,height=720)

2.3.2 LDA on Lv1

lda.fit <- 
  lapply(list(pcaL[[1]]$x[,1:elB[[1]][2]],
              pcaL[[2]]$x[,1:elB[[2]][2]]),
                function(y) {
                  lda(tr ~ ., data = as.data.frame(y))
                })

titlesvor <- paste("LDA decision boundaries for", paste0("C", 1:2))
voronoidf <- lapply(lapply(lda.fit, '[[', 3), data.frame)

#This creates the voronoi line segments

par(mfrow = c(1,2))
for(i in 1:length(pcaL)){
  plot(pcaL[[i]]$x[,1:2], col=ccol3[ford], pch=20, cex=1.5)
  title(titlesvor[i])
  text(pcaL[[i]]$x[,1:2], labels=rownames(pcaL[[i]]$x), 
       pos=ifelse(pcaL[[i]]$x[,1]<max(pcaL[[i]]$x[,1] -0.5),4,2), 
       col=ccol3[ford], cex=1.2)

  deldir(x = voronoidf[[i]][,1],y = voronoidf[[i]][,2], rw = c(-15,15,-15,15), 
       plotit=TRUE, add=TRUE, wl='te')
  text(voronoidf[[i]], labels=rownames(voronoidf[[i]]), cex=1.5, pos=1)
}

Figure 12: Voronoi diagrams on class means from LDA on PCA of untransformed correlation matrices

2.4 Clusters and Spatial Location (Lv 1)

Using the location data and the results of K-means++ we show a 3d scatter plot colored accoding to cluster.

set.seed(2^12)
s1 <- sample(dim(loc)[1],5e4)

locs1 <- loc[s1,]
locs1$cluster <- L[[1]][s1]

plot3d(locs1$V1,locs1$V2,locs1$V3,
       col=brewer.pal(4,"Set1")[order(table(L[[1]]))][locs1$cluster],
       alpha=0.75,
       xlab='x', 
       ylab='y', 
       zlab='z')

subid <- currentSubscene3d()
rglwidget(elementId="plot3dLocations", height=720, width=720)

3 Level 2: K-means++ for \(K=2\).

3.1 Heat maps (Lv 2):

## Formatting data for heatmap
aggp2 <- aggregate(dat,by=list(lab=L[[2]]),FUN=function(x){mean(x)}) 
aggp2 <- as.matrix(aggp2[,-1])[, ford]
rownames(aggp2) <- clusterFraction(L[[2]])

The following are heatmaps generated from clustering via K-means++

heatmap.2(as.matrix(aggp2),dendrogram='row',Colv=NA,trace="none", col=mycol,colCol=ccol[ford],cexRow=0.8, keysize=1.25,symkey=FALSE,symbreaks=FALSE,scale="none", srtCol=90,main="Heatmap of `fs` data.") 

Figure 13: Heatmap of the cluster means vs channels. Rows and columns are rearranged according to synapse type.

Percentage of data within cluster is presented on the right side of the heatmap.

3.2 Jittered scatter plot: Lv 2

ggCol <- brewer.pal(8,"Set1")[order(table(L[[2]]))]
cf2 <- data.frame(cf = clusterFraction(L[[2]]))

ggJ2 <- 
  ggplot(data = ggJdat, aes(x = ind, y = values, 
                         color = as.factor(lv2))) +
  scale_color_manual(values=ggCol, name="Cluster") + 
  geom_point(alpha=0.25, position=position_jitterdodge()) + 
  geom_boxplot(alpha =0.35, outlier.color = 'NA') + 
  annotate("text", x = levels(ggJdat$ind)[c(2,8,14,20)], y = 1.15*max(ggJdat$values), 
           label= cf2[1:4,]) + 
  theme(axis.title.x = element_blank()) + 
  theme(axis.text.x = element_text(color = ccol[ford], 
                                   angle=45,
                                   vjust = 0.5))

print(ggJ2)

Figure 14: Scatter Plot Level 2

The fraction of data points within each cluster are given at the top of the plot window.

3.3 Within cluster correlations (Lv 2)

corLV2 <- lapply(c(1:4),function(x){cor(dat[L[[2]] == x,])[ford, ford]})

difCor1112 <- ((corLV2[[1]] - corLV2[[2]]))
difCor2122 <- ((corLV2[[3]] - corLV2[[4]]))

layout(matrix(c(1,2,3,3,4,5,6,6), 4, 2, byrow=TRUE))
corrplot(corLV2[[1]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,3,0))
title("Cluster 1")
corrplot(corLV2[[2]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,3,0))
title("Cluster 2")
corrplot(difCor1112, method="color", tl.col=ccol[ford], 
         tl.cex=0.8,
         mar = c(0,0,3,0),
         cl.lim = c(min(difCor1112,difCor2122),max(difCor1112,difCor2122)),
         col=colorRampPalette(c("#998ec3", 
                                "white",
                                "darkorange"))(100))
title("Difference(1,2)")
corrplot(corLV2[[3]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,3,0))
title("Cluster 3")
corrplot(corLV2[[4]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,3,0))
title("Cluster 4")
corrplot(difCor2122, method="color", tl.col=ccol[ford], 
         tl.cex=0.8,
         mar=c(0,0,3,0),
         cl.lim = c(min(difCor1112,difCor2122),max(difCor1112,difCor2122)),
         col=colorRampPalette(c("#998ec3", 
                                "white",
                                "darkorange"))(100))
title("Difference(3,4)")

Figure 15: Within cluster correlations for level 2. (c11, c12, c21, c22) with differences

3.4 PCA of the within cluster correlation matrices at level 2.

pcaL <- lapply(corLV2, prcomp, center=TRUE, scale=TRUE)
elB <- lapply(pcaL, function(x) {getElbows(x$sdev, plot=FALSE)})
pcaLel2 <- mapply(function(x,y){ x$x[,1:y[2]] }, pcaL, elB)

3.5 LDA on Lv 2

lda.fit <- 
  lapply(pcaLel2, 
         function(y) {
                  lda(tr ~ ., data = as.data.frame(y))
                })

titlesvor <- paste("LDA decision boundaries for", paste0("C", 1:4))
voronoidf <- lapply(lapply(lda.fit, '[[', 3), data.frame)

#This creates the voronoi line segments

par(mfrow = c(2,2))
for(i in 1:length(pcaL)){
  plot(pcaL[[i]]$x[,1:2], col=ccol3[ford], pch=20, cex=1.5)
  title(titlesvor[i])
  text(pcaL[[i]]$x[,1:2], labels=rownames(pcaL[[i]]$x), 
       pos=ifelse(pcaL[[i]]$x[,1]<max(pcaL[[i]]$x[,1] -0.5),4,2), 
       col=ccol3[ford], cex=1.2)

  deldir(x = voronoidf[[i]][,1],y = voronoidf[[i]][,2], rw = c(-15,15,-15,15), 
       plotit=TRUE, add=TRUE, wl='te')
  text(voronoidf[[i]], labels=rownames(voronoidf[[i]]), cex=1.5, pos=1)
}

Figure 17: Voronoi diagrams on class means from LDA on PCA of untransformed correlation matrices

3.6 Clusters and Spatial Location (Lv 2)

Using the location data and the results of K-means++ we show a 3d scatter plot colored according to cluster.

set.seed(2^12)
s1 <- sample(dim(loc)[1],5e4)

locs2 <- loc[s1,]
locs2$cluster <- L[[2]][s1]

YlOrBr <- c("#FFFFD4", "#FED98E", "#FE9929", "#D95F0E", "#993404")
col.pal <- colorRampPalette(YlOrBr)

plot3d(locs2$V1,locs2$V2,locs2$V3,
       #col=colorpanel(8,"brown","blue")[order(table(L[[2]]))][locs2$cluster],
       col=col.pal(8)[-seq(1,8,2)][order(table(L[[2]]))][locs2$cluster],
       alpha=0.75,
       xlab='x', 
       ylab='y', 
       zlab='z'
       )

subid <- currentSubscene3d()
rglwidget(elementId="plot3dLocationsLV2", height=720, width=720)

4 Level 3: K-means++ for \(K=2\).

4.1 Heat maps (Lv 3):

## Formatting data for heatmap
aggp3 <- aggregate(dat,by=list(lab=L[[3]]),FUN=function(x){mean(x)})
aggp3 <- as.matrix(aggp3[,-1])[, ford]
rownames(aggp3) <- clusterFraction(L[[3]])

The following are heatmaps generated from clustering via K-means++

heatmap.2(as.matrix(aggp3),dendrogram='row',Colv=NA,trace="none", col=mycol,colCol=ccol[ford],cexRow=0.8, keysize=1.25,symkey=FALSE,symbreaks=FALSE,scale="none", srtCol=90,main="Heatmap of `fs` data.") 

Figure 18: Heatmap of the cluster means vs channels. Rows and columns are rearranged according to synapse type.

Percentage of data within cluster is presented on the right side of the heatmap.

4.2 Jittered scatter plot: Lv 3

ggCol <- brewer.pal(8,"Set1")[order(table(L[[3]]))]
cf3 <- data.frame(cf = clusterFraction(L[[3]]))

ggJ3 <- 
  ggplot(data = ggJdat, aes(x = ind, y = values, 
                         color = as.factor(lv3))) +
  scale_color_manual(values=ggCol, name="Cluster") + 
  geom_point(alpha=0.25, position=position_jitterdodge()) + 
  geom_boxplot(alpha =0.35, outlier.color = 'NA') + 
  annotate("text", x = levels(ggJdat$ind)[seq(2,22,length=8)], y = 1.05*max(ggJdat$values), 
           label= cf3[1:8,]) + 
  #geom_jitter(width=2) + 
  theme(axis.title.x = element_blank()) + 
  theme(axis.text.x = element_text(color = ccol[ford], 
                                   angle=45,
                                   vjust = 0.5))

print(ggJ3)

Figure 19: Scatter Plot Level 3

4.3 Within cluster correlations (Lv 3)

corLV3 <- lapply(c(1:8),function(x){cor(dat[L[[3]] == x,])[ford, ford]})

difCor1 <- (corLV3[[1]] - corLV3[[2]])
difCor2 <- (corLV3[[3]] - corLV3[[4]])
difCor3 <- (corLV3[[5]] - corLV3[[6]])
difCor4 <- (corLV3[[7]] - corLV3[[8]])
M <- max(difCor1, difCor2, difCor3, difCor4)
m <- min(difCor1, difCor2, difCor3, difCor4)

layout(matrix(c(1, 2, 3, 3,
                4, 5, 6, 6, 
                7, 8, 9, 9,
                10, 11, 12, 12), 8,2, byrow=TRUE))

corrplot(corLV3[[1]],method="color",tl.col=ccol[ford], tl.cex=0.8,
         mar=c(0,0,3,0))
title('Cluster 1')
corrplot(corLV3[[2]],method="color",tl.col=ccol[ford], tl.cex=0.8,
         mar=c(0,0,3,0))
title('Cluster 2')
corrplot(difCor1,method="color",tl.col=ccol[ford], tl.cex=0.8,
         cl.lim=c(m,M), 
         mar=c(0,0,3,0),
         col=colorRampPalette(c("#998ec3",
                                "white",
                                "darkorange"))(50))
title('Difference(1,2)')
corrplot(corLV3[[3]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,3,0))
title('Cluster 3')
corrplot(corLV3[[4]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,3,0))
title('Cluster 4')
corrplot(difCor2,method="color",tl.col=ccol[ford], tl.cex=0.8, 
         cl.lim= c(m,M),
         mar=c(0,0,3,0),
         col=colorRampPalette(c("#998ec3",
                                "white",
                                "darkorange"))(50))
title('Difference(3,4)')
corrplot(corLV3[[5]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,3,0))
title('Cluster 5')
corrplot(corLV3[[6]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,3,0))
title('Cluster 6')
corrplot(difCor3,method="color",tl.col=ccol[ford], tl.cex=0.8,
         cl.lim= c(m,M),
         mar=c(0,0,3,0),
         col=colorRampPalette(c("#998ec3",
                                "white",
                                "darkorange"))(50))
title('Difference(5,6)')
corrplot(corLV3[[7]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,3,0))
title('Cluster 7')
corrplot(corLV3[[8]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,3,0))
title('Cluster 8')
corrplot(difCor4,method="color",tl.col=ccol[ford], tl.cex=0.8,
         cl.lim= c(m,M),
         mar=c(0,0,3,0),
         col=colorRampPalette(c("#998ec3",
                                "white",
                                "darkorange"))(50))
title('Difference(7,8)')

Figure 20: Within cluster correlations for level 3. (c111, c112, c121, c122, c211, c212, c221, c222)

4.4 PCA of the within cluster correlation matrices at level 3.

pcaL <- lapply(corLV3, prcomp, center=TRUE, scale=TRUE)
elB <- lapply(pcaL, function(x) {getElbows(x$sdev, plot=FALSE)})
pcaLel3 <- mapply(function(x,y){ x$x[,1:y[2]] }, pcaL, elB)

4.5 LDA on Lv 3

lda.fit <- 
  lapply(pcaLel3, 
         function(y) {
                  lda(tr ~ ., data = as.data.frame(y))
                })

titlesvor <- paste("LDA decision boundaries for", paste0("C", 1:8))
voronoidf <- lapply(lapply(lda.fit, '[[', 3), data.frame)

#This creates the voronoi line segments

par(mfrow = c(4,2))
for(i in 1:length(pcaL)){
  plot(pcaL[[i]]$x[,1:2], col=ccol3[ford], pch=20, cex=1.5)
  title(titlesvor[i])
  text(pcaL[[i]]$x[,1:2], labels=rownames(pcaL[[i]]$x), 
       pos=ifelse(pcaL[[i]]$x[,1]<max(pcaL[[i]]$x[,1] -0.5),4,2), 
       col=ccol3[ford], cex=1.2)

  deldir(x = voronoidf[[i]][,1],y = voronoidf[[i]][,2], rw = c(-15,15,-15,15), 
       plotit=TRUE, add=TRUE, wl='te')
  text(voronoidf[[i]], labels=rownames(voronoidf[[i]]), cex=1.5, pos=1)
}

Figure 21: Voronoi diagrams on class means from LDA on PCA of untransformed correlation matrices

4.6 Clusters and Spatial Location (Lv 3)

Using the location data and the results of K-means++ we show a 3d scatter plot colored according to cluster.

set.seed(2^12)
s1 <- sample(dim(loc)[1],5e4)

locs3 <- loc[s1,]
locs3$cluster <- L[[3]][s1]

plot3d(locs3$V1,locs3$V2,locs3$V3,
       col=col.pal(16)[-seq(1,8,2)][order(table(L[[3]]))][locs3$cluster],
       alpha=0.65,
       xlab='x', 
       ylab='y', 
       zlab='z'
       )

subid <- currentSubscene3d()
rglwidget(elementId="plot3dLocationsLV3", height=720, width=720)

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